Drag on a liquid-infused superhydrophobic cylinder

We examine the effect of liquid-infused superhydrophobic surfaces on the separation over a circular cylinder for Reynolds numbers $400 < Re_D < 1700$. Two superhydrophobic surfaces are compared with a smooth untreated surface. A thin lubricant film (1-20 microns in thickness) is applied to a surface with isotropic nanoscale texture and also to a surface with 50 $\mu$m-deep, 65 $\mu$m-wide triangular grooves aligned with the flow. The viscosity and thickness of the lubricant are varied. With a superhydrophobic surface, the drag increases by 0 to 5\%; greater drag is experienced by the microstructured surface. Drag does not appear to depend on the thickness of the overlying lubricant. In contrast to superhydrophobic surfaces with gas-filled cavities, liquid-infused surfaces produce no change in the Strouhal number. The source of the drag increase is rationalized using the structure of the measured velocity fields near the cylinder.